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Dynamics of a rolling robot.

K I Ilin1, H K Moffatt2, V A Vladimirov1,3

  • 1Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdom.

Proceedings of the National Academy of Sciences of the United States of America
|November 22, 2017
PubMed
Summary

This study models a rolling ball with an internal rotor, revealing chaotic motion tendencies as rotor orbit radius increases. Experiments confirm these chaotic dynamics in a rolling spherical shell system.

Keywords:
chaotic rollinginternal rotornonholonomic systemrolling robot

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Area of Science:

  • * Physics
  • * Mechanical Engineering
  • * Dynamical Systems

Background:

  • * Investigates the complex dynamics of rolling bodies.
  • * Explores systems with internal moving masses influencing external motion.
  • * Addresses the need for understanding nonholonomic systems in mechanics.

Purpose of the Study:

  • * To derive and analyze the equations of motion for a rolling spherical shell with an internal rotor.
  • * To investigate the conditions leading to chaotic behavior in this system.
  • * To validate theoretical predictions through experimental observation.

Main Methods:

  • * Developed a mathematical model for a spherical ball with an internal rotor.
  • * Formulated a six-dimensional, nonholonomic, nonautonomous dynamical system.
  • * Employed numerical integration to explore parameter space and initial conditions.
  • * Conducted physical experiments to observe the predicted behaviors.

Main Results:

  • * Identified four key dimensionless parameters governing the system's dynamics.
  • * Demonstrated a tendency towards chaotic motion with increasing rotor orbit radius.
  • * Found specific initial angular velocities that induce chaotic trajectories while maintaining contact.
  • * Observed chaotic behavior experimentally, consistent with numerical predictions.

Conclusions:

  • * The rolling spherical shell with an internal rotor exhibits complex, potentially chaotic dynamics.
  • * System parameters, particularly rotor orbit radius and initial angular velocity, critically influence motion.
  • * The study provides a framework for understanding and predicting chaotic phenomena in similar mechanical systems.